ap stats study guides

โœŒ๏ธย  Unit 2 - Exploring Two-Variable Data

โš–๏ธย  Unit 6 - Inference for Categorical Data: Proportions

๐Ÿ˜ผย  Unit 7 - Inference for Qualitative Data: Means

โœณ๏ธย  Unit 8 Inference for Categorical Data: Chi-Square

๐Ÿ“ˆย  Unit 9 - Inference for Quantitative Data: Slopes

๐Ÿงย  Multiple Choice Questions (MCQs)

4.11 Parameters for a Binomial Distribution

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โฑ๏ธย ย 2 min read

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kanya shah


In order to use binomial formulae for mean and standard deviation, you need to identify whether the conditions qualify for binomial distribution. If one of four conditions donโ€™t work/occur, it is not a binomial setting. In other words, you canโ€™t just use binomial distribution because you feel like it. 10% Condition: When taking a random sample of size n from a population of size N. we can use a binomial distribution to model the count of successes in the sample as long as n < 0.10N.

The four conditions for a binomial setting are Binary, Independent, Number, and Same Probability or BINS. Remember your BINS for the AP Stats exam questions.ย 

  • Binary: The possible outcomes of each trial can be classified as a success or a failure.ย 

  • Independent: Trials must be independent. That is, knowing the outcome of one trial must not tell us anything about the outcome of any other trial.ย 

  • Number: The number of trials n of the chance process must be fixed in advance.ย 

  • Same Probability: There is the same probability of success p on each trial.ย 

Describing Mean and Standard Deviation of Binomial Variables

Disclaimer: These formulae only work for binomial settings!

To find the mean of a binomial random variable: If a count X of successes has a binomial distribution with number of trials n and probability of success p, the mean (expected value) of X is mean = n*P.ย 

To find the standard deviation of a binomial random variable: If a count X of successes has a binomial distribution with number of trials n and probability of success p, the standard deviation of X is standard deviation = np(1-p).ย 

Binomial Distributions in Statistical Sampling:ย 

10% Condition: When taking a random sample of size n from a population of size N. we can use a binomial distribution to model the count of successes in the sample as long as n < 0.10N.

๐ŸŽฅWatch: AP Stats - Probability: Random Variables, Binomial/Geometric Distributions

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